What is the Fibonacci Sequence & the Golden Ratio? Simple Explanation and Examples in Everyday Life

The Fibonacci sequence is a series of numbers in which a given number is the addition of the two numbers before it. So, if you start with 0, the next number will be 1, followed by 1, followed by 2, followed by 3 and so on. As you can see, every number in this series or sequence is obtained by adding the two preceding numbers. This simple series of numbers is referred to as the Fibonacci sequence for Fibonacci series. And individual numbers in this sequence are often called Fibonacci numbers.
To the uninitiated, it may just seem like a series of numbers, but the Fibonacci sequence has been discovered and rediscovered in various forms, not only in mathematics, but also in nature and our everyday lives.
There’s another exciting offshoot of the Fibonacci sequence - the golden ratio. Seashells are one of the most common examples of the golden spiral in nature. Ocean waves, hurricanes, flower buds, snail shells, spider webs are some of the many naturally-occurring examples.
#science #animation #fibonacci
Intro - (0:00)
What is the Fibonacci sequence - (0:57)
Leonardo of Pisa and the Fibonacci sequence - (1:39)
Fibonacci sequence and the Golden Ratio - (2:56)
References:
math.temple.edu/~reich/Fib/fi...
brilliant.org/wiki/fibonacci-...
Original Article Link: www.scienceabc.com/eyeopeners...
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[@allisonnowak3609]

It bothers me that the visuals show the incorrect sequence (0, 1, 2, 3...). Shouldn't it be 0, 1, 1, 2, 3...? (Example of incorrect at 1:35 and 2:36.)

[@Scienceabc]

Yes. You are right. Thanks for pointing out.

[@snarecat3441]

It did show 0 11 on the first example I believe

[@zamzamkoena1077]

@allisonnowak3609, He did show 0,1,1, 2... right at the beginning. I am happy with his explanation, especially the real-life examples.

[@stevenseiders8731]

It can be either since 0 really isn't a +or-number

[@stevenseiders8731]

This explanation is acceptable.

[@gmwell1]

Excellent presentation, the one place that everybody seems to miss is that the Fibonacci sequence is also found inside the programming of the human brain, your brain automatically tells you whether somebody's face and body fits inside the Fibonacci sequence because you determine them to be handsome or pretty based on the closeness of the math formula in the facial structures or the body... So if the eyes are too far apart and the ears are not in the right place your brains programming automatically tells you that person's out of mathematical Harmony.. the Divine ratio programmed in the brain.

[@angeltapia5675]

Thanks for sharing

[@worldisfilledb]

That’s a huge assumption, nothing to back that up

[@gmwell1]

@@worldisfilledb lol your comments not even worth replying to it's so foolish and silly

[@patyso5617]

Why do women like ugly men?

[@BejaranoAngeles.11.]

That is called the Golden Ratio

[@amans4844]

The Indian guy on the bike is awesome

[@Scienceabc]

He's our favorite too :)

[@deeptanudey6631]

He is Mathematician Pingala

[@thomasjp5847]

@@deeptanudey6631 Nailed it lol

[@raxter7cr88]

How come dey name it hindu Arabic 🤦😂

[@satyakisil9711]

@@raxter7cr88 why not?

[@DineshKumar-uw9fp]

Beautifully presented and very well elaborated. "SHORT AND PRECISE"!! This video is so easy to understand the Fibonacci sequence and the golden ratio. Good Work!!

[@raxter7cr88]

Deres no word like hindu arabic system dude! Ancient india had no linkage to arab World 😒

[@johndavis6576]

It was well presented but I'm stuck on something he said. I work construction as a labourer on sites, I'm no architect, but how does the golden spiral help in the design of a new building when creating it.

[@ivxn8216]

@@johndavis6576 iu

[@avtpro]

I never called it Fibonacci, just the Golden Ratio. Learned something new. Thanks.

[@Anamnesis]

You left out financial markets. Fibonacci retracement is a technical analysis method used to predict (with alarming accuracy) the various levels of support and resistance when trading equities and assets. It isn't portrayed as a spiral on a pricing chart, but the ratio principle remains the same. And since markets are ultimately an indicator about public sentiment over the value of something, it shows how the Fibonacci Sequence applies to human psychology and emotion too.

[@luhcollins]

YOU. I found you. You are the author of the exact comment I was looking for. ALARMING accuracy is right,

[@thomasjp5847]

The Golden ratio is often applied to the stock market.

[@oliverhawkins6487]

Is the alarming accuracy because traders are all looking out for it though? So will set their bids/sell orders at these levels.

[@luhcollins]

@@oliverhawkins6487 very possible , its also simple to program a computer to buy retracements based on percentages. It likely works due to a combination of algorithms and common-acceptance amongst traders

[@fouadmas5413]

It's also in our DNA SEQUENCE

[@KenMiddletonUkulele]

In music e.g. intervals between the notes of the major chord, notes of the harmonic series on brass instruments, serial (12 tone) music, etc.

[@shoecake6303]

I love this. The workings of the universe in an equation. When I first heard of this, I couldn’t help but to count petals, and would tell anyone who’d listen!

[@_s1591]

I forgot when I subscribed to this channel and this is the first video I viewed after subscribing, I really like it.Our professor taught us how to write Fibonacci sequence in c

[@Scienceabc]

A computer programming class is where most of us first learn about it. But the deeper you get into it, you realize how fascinating it is. And it has much more to offer to us humans than just an algorithm to learn how to code. We are glad you liked it :).

[@Scienceabc]

Do you encounter the golden ratio in your everyday life? If you have some more examples, then do share them with others in the comment section below.

[@moirapettifr7127]

My pet dog.

[@ahmedmac3142]

The ratio of the total number of chapters in the Quran (114) which represents the physical design of the Quran divided by the Quran Constant (70.44911244) which represents the mathematical design of the Quran gives 1.6181893; it is amazingly almost equal to the golden ratio

[@RoPavatar]

A steel ball maybe

[@carlosalexandreFAT]

The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum). Ramanujan number: 1,729 Earth's equatorial radius: 6,378 km. Golden number: 1.61803... • (1,729 x 6,378 x (10^-3)) ^1.61803 x (10^-3) = 3,474.18 Moon's diameter: 3,474 km. Ramanujan number: 1,729 Speed of light: 299,792,458 m/s Earth's Equatorial Diameter: 12,756 km. Earth's Equatorial Radius: 6,378 km. • (1,729 x 299,792,458) / 12,756 / 6,378) = 6,371 Earth's average radius: 6,371 km. The Cubit The cubit = Pi - phi^2 = 0.5236 Lunar distance: 384,400 km. (0.5236 x (10^6) - 384,400) x 10 = 1,392,000 Sun´s diameter: 1,392,000 km. Higgs Boson: 125.35 (GeV) Phi: 1.61803... (125.35 x (10^-1) - 1.61803) x (10^3) = 10,916.97 Circumference of the Moon: 10,916 km. Golden number: 1.618 Golden Angle: 137.5 Earth's equatorial radius: 6,378 Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2. (((1.618 ^137.5) / 6,378) / 6.67) x (10^-20) = 12,756.62 Earth’s equatorial diameter: 12,756 km. The Euler Number is approximately: 2.71828... Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ (2.71828 ^ 6.67) x 1.618 x 10 = 12,756.23 Earth’s equatorial diameter: 12,756 km. Planck’s constant: 6.63 × 10-34 m2 kg. Circumference of the Moon: 10,916. Gold equation: 1,618 ɸ (((6.63 ^ (10,916 x 10^-4 )) x 1.618 x (10^3)= 12,756.82 Earth’s equatorial diameter: 12,756 km. Planck's temperature: 1.41679 x 10^32 Kelvin. Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Speed of Sound: 340.29 m/s (1.41679 ^ 6.67) x 340.29 - 1 = 3,474.81 Moon's diameter:: 3,474 km. Cosmic microwave background radiation 2.725 kelvins ,160.4 GHz, Pi: 3.14 Earth's polar radius: 6,357 km. ((2,725 x 160.4) / 3.14 x (10^4) - (6,357 x 10^-3) = 1,392,000 The diameter of the Sun: 1,392,000 km. Numbers 3, 6 & 9 - Nikola Tesla One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km. The Numbers: 3, 6 and 9 ((3^6) x 9) - (3.086 x (10^3)) -1 = 3,474 The Moon's diameter: 3,474 km. Now we will use the diameter of the Moon. Moon's diameter: 3,474 km. (3.474 + 369 + 1) x (10^2) = 384,400 The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384,400 km. Moon's diameter: 3,474 km. ((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3,474 = 6,378 Earth's equatorial radius: 6,378 km. Orion: The Connection between Heaven and Earth eBook

[@daniesavage]

I love that it dates back to the 6th century in India. I wonder how long it’s been studied. Love the history of science. Shouts out to India and any other culture who may have known about this ❤. Fascinating 🐌🐌

[@Junkinsally]

The only reason matter manifests as a spiral is because the universe and everything in it are spinning. The “divine ratio” is just a visual representation of the rate of that spin.

[@BejaranoAngeles.11.]

Actual life vibration..... look up youtube videos where vibration of sound is recorded in Sand, water and fire, and lastly electricity....all done and shown from the vibration of music, it is mind blowing and life changing.... Is complete proof that real vibration makes the shapes.....uncomfortable sounds made actual ugly shapes in the sand, where beautiful music made absolute divine complex shapes in the sand.... all these shapes are exact formations of many complex Crop Circles..... also with the vibrational shapes the music made with the water....and sand....well effects us WATER BEINGS TREMENDOUSLY !!!!!! all sounds have vibrational frequency including peoples voices which cause actual structural shapes within us, being made up of so much sodium water, it is just fascinating and never ending and forever

[@fgdart]

Great work! I watched many videos byt this one was very clear and well explained! Thank you

[@mohanpathak]

All animations are supreme. Such an informative and entertaining video. You make a great contribution to science.

[@Scienceabc]

Thanks a lot for the comment. We are glad that you liked it. Do subscribe and share it with your friends please.

[@BejaranoAngeles.11.]

Look up here on youtube the vibratiinal proof of how sound and vibration actually take form and shape...LOOK UP (NIGEL MUSIC) CYMATICS.....BRINGS THIS MORE TOGETHER .....

[@williamseifert169]

Use this ratio when you're brewing your coffee and you will achieve the perfect cup. For example, 1.6 tablespoons of coffee grounds per 6 oz of water. If you use Kcups, which have about 2 tablespoons of grounds in them, then the ratio is 1 Kcup per 7.5 ounces of water. You're welcome.

[@spicyacai]

How would it be using the metric system?

[@SevenTheMisgiven]

You would be arrested for witchcraft if you carried this formula around like that.

[@jefersonmachado6775]

Excellent teaching, Fibonacci also has full application in financial assets, mainly on the Index, and high volatility assets.

[@bakedfortgod8241]

Explain further plz

[@Mark.Allen1111]

@@bakedfortgod8241 The Dow goes up 70% of the time. It goes down 30% of the time. That’s why if you sell you have a greater chance of losing. Just buy and hold the S&P 500.

[@Music_is_Breathing]

Thank you! You did an excellent job of explaining the Fibonacci sequence and the Golden Ratio so dummies like me can understand it. more or less.

[@JULO-I]

Very interesting concept. Thanks for the explanation.

[@waywardboundband8716]

I bought my wife an ammolite(opalized ammonite) pendant for her up coming birthday. It's a spectacular example of the golden ratio!

[@shaheerakonoth8166]

I have an upcoming math competition at a secondary school and this has helped me understand Fibonacci (It was also beautifully presented)

[@dokepravin2916]

Excellent. Truly a masterpiece. It was an eye opener.

[@mayahewitt9261]

Now I can learn to spin my steel balls

[@mayahewitt9261]

@@altoid211 to defeat president Valentine

[@mikewright3029]

finally an easy explanation.. Thank you. I swear some people just talk. lol

[@chimpmonk]

im sorry, im not really intelligent, but i can't seem to figure out 4:33, how or where exactly do you see the spiral? Even with the guidelines, i still can't figure it out

[@0pini0n21]

They are not guide lines ...You just have join the corners of all rectangles inside the the bigger rectangle which is divided in 1.618 proportion (golden ratio) and you'll get the Golden Spiral Also, the golden spiral is infinite

[@chimpmonk]

@@0pini0n21 oh ok i see it, thank you for explaining 👊🏽

[@user-pq9yd8fr4m]

Lots of 😃 😀 😄 great

[@brundabatibarik9180]

I'm here after gate, 2024 (physical science) and regretting why didn't I watch it before.

[@Cloud-Radio]

thats how concepts came from world to books ...nowadays everyone is stop observing and forgetting how to read the world around us.

[@knatsomitab7376]

My personal favorite; pine cones. Especially visible with the female cones.

[@dradman7677]

Very useful for trading, crypto's and such 😉

[@KushagraPratap]

Wowowoowowow I love discovering new things like this and short too. Please keep such videos coming 😀

[@Scienceabc]

More to come for sure! Glad you liked it. Do share it with your friends.

[@KushagraPratap]

@@Scienceabc yeah sure :D

[@Scienceabc]

Thanks a lot. That will be a great help.

[@celestineP]

If it was described by Indians in the 6th Century, and Fibonacci merely translated the concepts, shouldn’t it be called by the original name - as the Pingala sequence?

[@emilymalinowski5027]

I think it's too late now but I see where you are coming from

[@ApocalypseIsNow]

No.

[@zgb3l]

Both names are just a way to identify this theorem, so just call it whatever you relate it with i guess

[@twenty-fifth420]

@@zgb3l Synonyms are based, we need more of them. The more ‘names’ you know for the ‘words’ like/use, the more learn or something like that.

[@__Creative_art_and_craft__]

It was buddist monk who worked in nalanda

[@ianbudgetrc2574]

Thank you for this video. Made me understand everything. I have this hobby called RC speed running. So, I always convert mph to kph. It's just funny because coincidentally, 1 mile = 1.609 kilometres. 1.609 is close to 1.618033 😁

[@herwigmenzel5179]

The numbers of 13 21 34 55 multiplied together = 510510 which is the product of the 1st 7 prime numbers 2 3 5 7 11 13 and 17

[@parakramsingh9788]

Mind blown🔥 Bravo Leanardo Pisano 👏

[@marekantonini5909]

Actually before Leonardo the fibonacci sequence where discover in India.

[@thecema7158]

Loved the visualisation and explaination for the ratio that rules all...😍😍

[@Scienceabc]

Thanks. Glad that you liked it. Do share it with your friends and subscribe to our channel.

[@sandywellsart]

How do you find the ratio of A & B so that you proceed to find out if it equals the sum? Thank you

[@shorttking2074]

divide a and b

[@martincart2775]

My favorite example is in the structure of the song 'Lateralus' by Tool.

[@aishwaryaagarwal9709]

first video which tells the actual truth about the invention of Fibonacci series in India😍

[@MrSweetheartforever]

I 'm a beginner...more please!

[@user-uu2vf2mo9v]

I love how nothing I learned about math in school was ever any interesting. Ha!

[@drsuuzihazen]

We have seen it in the leaves of cacti. And the shape of jars.

[@charithaw4232]

Great explanation! Thank you so much 🙏

[@Scienceabc]

Glad it was helpful!

[@jerromeploya6294]

This is the best and simple explanation so far!!!! :)

[@Scienceabc]

Glad you think so!

[@altarush]

What about dog’s eyes, a great white shark’s jaw, and rows of teeth? I might be wrong wrong though, and maybe I found a perfect triangle with a shark’s tooth.

[@YoReLa72]

Thank you for sharing. I'm sending to my friends who home school.

[@Scienceabc]

Awesome! Thank you!

[@pollos1]

Gyro would love this

[@OceanusAscend18]

The one who came up with this discovery was guru Pingala.

[@mrindia1]

I am curious what a 0 Fibonacci looks like tho. Has to be there too right?

[@SanjayBorad]

Very Good video. the explanation is very clear. Keep making such videos.

[@Scienceabc]

Thanks a lot Sanjay. We are glad that you liked the video. Do subscribe to our channel and share the video with your friends.

[@SanjayBorad]

@@Scienceabc sure will share it with my friends.

[@Scienceabc]

Thanks a lot for that.

[@esa9289]

Hi! Thank you for sharing your knowledge! Can we use this video for our research as one of our sources? Surely we will greatly appreciate your consent and we’ll make sure to cite your video properly. Thanks!

[@Scienceabc]

Sure. As long as you give proper credits you can use it as part of your research.

[@musfiqueryeead]

Fascinating Fibonacci ❤️

[@MsMlbmlb]

The golden ratio curve is the same as the one calculated when annealing glass.

[@maripol9102]

Is a cauliflower pattern an example of Fibonacci's sequence?

[@daroslawdaroslawski]

its simple explanation - cosmos. vibration, pattern. Sound of the universe. theory created by the artist Dariusz Stolarzyn, simple.

[@apostolarlseugene4522]

Why is it that Fibonacci starts his famous sequence with numbers 1 and 1? Can you tell the story behind this?

[@DoomFinger511]

because 0+1=1 but 0 is not technically a number. Only in computers is 0 consider a valid number (or NULL or OFF) which is why in computing base 10 is not 1-10 but 0-9.

[@zamzamkoena1077]

So clear. Thank you so much.

[@Scienceabc]

Glad it was helpful!

[@KM-qn9ys]

This video deserve more views. thanks for this creation... 😍

[@Scienceabc]

Thank you so much 😀

[@emresagdik7479]

Amazing video

[@kluchtube7042]

great demonstration!

[@OneCatholicSpeaks]

Popular culture example. In Star Trek (1960s). The Producers openly stated the the Golden Ratio was used in designing the proportions of The Enterprie (featured space craft).

[@Hampvs23]

Because the sequence is the movement of time in space. Time constantly moves, and looking at a clock we can measure time with a circle with 2 moving indicators, so the time moves but not the space. The sequence however is allways a spiral, we look at it as numbers and a still picture. But what if the sequence actually is the movement of time in space? And the "middle" is the present wich allways moves towards the future and the wider ares of the frequence is the past, the previous numbers. What if we can calculate the future by observeing the numbers in the frequence according to time? That way we know when the "3" is next up in the frequence we can look back at the last "3" to know what will happen in the future "3". I'm just yapping but I thought it was a cool thought! Edit: the golden ratio (the spiral) is present in all things, all things grow or evolve with time, it grew from one point into the full being of it's being and it still grows unless it dies or has reached a limit.

[@Hampvs23]

Example if an artist paints a banana, the sequence has reached it's limit unless he decides to continue adding to the painting, that way the sequence will continue to grow, by adding paint wich in turn is depended on the time it takes to add that part

[@curtpiazza1688]

Fascinating presentation! 😊

[@Scienceabc]

Glad you enjoyed it!

[@theintegratedguy9528]

Such an underrated channel 😢

[@Regularsshorts]

The is a ratio between the fibbonaci numbers its called golden ratio The golden ratio is 1:1.6

[@Scienceabc]

You're right

[@fmgh2153]

Most informative video of maths ever in simple explanation.👍🙏

[@Scienceabc]

Glad that you liked it.

[@deepakchoudhary8015]

Fibonacci took numerals from India… Newton took calculus from India… Oppenheimer invented Atomic bomb after getting inspired from Bhagwad Gita….Many modern physics laws r mentioned in our ancient Vedas….What to country to live…Really feel Proud of being an indian..😍😍😍

[@daniesavage]

Blessings to you and your culture 🇮🇳

[@afarensis79]

Einstein took relativity from India, Hawking took black holes from India, linguistics too language from India, civil engineering took cities from India, NASA took space shuttle from India, Edison took light bulb from India, Benjamin Franklin discovered electricity from lightning from clouds coming from India, Bill Gates took the PC from India, the rivers of the world take water from India, the atmosphere takes Oxygen from India, human race owes its existence to India, even UFO’s visit earth to praise India. Proud to come from India.

[@davidlamb7524]

Oppenheimer famously said "Now I am become death destroyer of worlds " which was paraphrasing the Baghvad Gita AFTER he saw the result of the first atomic bomb not before. So it had not inspired him in any way. Much credit to India where it is due. No need for such false claims, it has an extraordinary history of discovery.

[@deepakchoudhary8015]

@@davidlamb7524 why would an atomic scientist read any religious text…and on biggest achievement of his life he quoted phrase from that religious text which he not even belonged….m not saying that he discovered bomb after reading the bhagvad gita…..I said he was pretty much inspired from the book….

[@davidlamb7524]

@deepakchoudhary8015 He thought it a suitable phrase for the horror he had caused. d

[@naazgoel7148]

hey, thanks for this fun and interesting video that surely made my research a lot simpler. Also, what software do you use.??

[@Scienceabc]

We use Adobe animate to make these videos.

[@mikelombard21]

Well, the fibonnaci numbers do not have the golden ratio, I believe they chase the golden ratio in a sine wave getting ever closer to it. Which is wondrous in itself.

[@raycherry7074]

In another video, this result could be proven. Pretty advanced, but beautiful.

[@lauragordon4194]

We think a spiral staircase (in architecture) is also a Fibonacci sequence.

[@costrio]

Couldn't I just take a picture of the outline on a transparency and superimpose it upon a picture to reveal the sequence events. (One would have to zoom in and out of course to match the respective objects seen? I might try something like that to play with when I have some time to waste/play with.) It's not always easily discernible and I wonder at why they choose certain starting points, like the back of an apostle -- Judas perhaps? He could have put Jesus' heart from a different point of view, perhaps? Just wondering...

[@keziegullonan2343]

Kaway kaway sa mga college students na naririto for the sake of reflection hahaha.

[@amerebumpintheroad]

Have there been examples of these present in agates?

[@JenMarco]

This can be used with the stock market. I’m here to figure it out.

[@Makeshiftjunkbox]

Fibonacci sequence, Pi and the Golden Mean all interwoven came from the nature of a Cometary Lightbolt that was drawn into the dark depths of the Universe morphing into a round flat accretion disc on the whole warping into our present globus being the home of the point of singularity a primordial seed germinating the Universe yet to complete the first phase of its cycle!

[@softhoomann]

I have a question, is custard apple an example of fibonacci?

[@rishiagrawala]

found a very interesting coincidence by using chatgpt which is as follows ### Theorem: Proportions in a Prime-Derived Fibonacci-like Sequence Approaching the Golden Ratio **Statement:** Given a sequence of prime numbers arranged in ascending order, construct a Fibonacci-like sequence where each term is the sum of the two preceding terms. The proportions obtained by dividing each term by its subsequent term in this sequence will approach the golden ratio, \(\phi = \frac{1 + \sqrt{5}}{2} \approx 0.618\). **Proof:** 1. **Prime Sequence**: Consider a sorted list of prime numbers \( \{p_i\} \) in ascending order. 2. **Fibonacci-like Sequence Construction**: Construct a Fibonacci-like sequence \( \{F_n\} \) using the primes: \[ F_0 = p_0, \quad F_1 = p_1 \] \[ F_n = F_{n-1} + F_{n-2} \quad \text{for } n \geq 2 \] 3. **Example Sequence**: Using the prime numbers from the symmetric pairs: \[ 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803, 141422324, 228826127, 370248451, 599074578, 969323029, 1568397607, 2537720636, 4106118243, 6643838879 \] 4. **Proportions Calculation**: Calculate the proportions \( R_n \) by dividing each term by its subsequent term: \[ R_n = \frac{F_n}{F_{n+1}} \] These proportions are: \[ 0.636, 0.611, 0.621, 0.617, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618, 0.618 \] 5. **Limit of Proportions**: As \( n \) increases, the proportions \( R_n \) approach the golden ratio: \[ \lim_{n \to \infty} R_n = \phi = \frac{1 + \sqrt{5}}{2} \approx 0.618 \] 6. **Conclusion**: The proportions of each prime number divided by the subsequent prime number in the Fibonacci-like sequence constructed from the sorted prime numbers approach the golden ratio. Therefore, we have: \[ \boxed{\lim_{n \to \infty} \frac{F_n}{F_{n+1}} = \phi \approx 0.618} \] This theorem illustrates that the Fibonacci-like sequence derived from a sorted list of prime numbers exhibits the same convergence property as the classical Fibonacci sequence, with proportions approaching the golden ratio.

[@aathikaanas9858]

Nice video

[@NeerajKumar-qw4js]

ex of fibonacci sequence is= tornado

[@aqsashaheen1305]

This is really interesting. I am doing a class project on this.

[@blossoms4505]

Wow me too I guess mine is a seminar

[@waqaralishah5446]

What kinda of project and seminar! What's the outcome of it

[@blossoms4505]

@@waqaralishah5446 mine actually didnt happen bcz the teacher forgot about it😂

[@waqaralishah5446]

@@blossoms4505 lol

[@JWard-sp7wt]

Im not seeing it in that painting and building 🤨

[@Scienceabc]

The golden spiral is everywhere around you, you just need to pay close attention :)

[@tpacc123]

Very good explanation. And good examples too

[@Scienceabc]

Glad you liked it!

[@dakshayiniramesh8175]

Knitting of sweaters can also be an example of finonacci sequence

[@Cloud-nd2cm]

That's as clear as possible 👍

[@Scienceabc]

Glad you found it useful!

[@balonkita185]

It can also be used to heal cripples

[@surajvisana2025]

Did anyone noticed that distance between small end of spiral and long end of spiral is golden ratio. Anyone.

[@saihaansensei]

The inside of a watermelon when you cut it in half also has the Fibonacci sequence, i noticed.

[@sachinchaudhary1310]

thanks for mantioning india..

[@ranjeetkumar2051]

thank you sir for making this video

[@JuandelaCruz-zl1le]

This is why 4-leaf clover is so rare

[@aquilasanchez2352]

You can really tell that there is a divine Creator in all of this!

[@hollieyates6505]

Yes!

[@michael-vl1mn]

No, it is something to do with variable valency in elements The benzene ring in fuel is an example.

[@andreas2672]

The elephant was awesome :-)

[@shep1818]

I can finally use spin.

[@spsingh5857]

Its was discovered in india 1000 before hemachnadra

[@saifbhai52]

I like it very good

[@imissyou6365]

Once u see it u can’t unsee it.

[@Scienceabc]

You're absolutely right!

[@user-pq9yd8fr4m]

Beautifully told

[@user-ru4bk6ro1j]

Nice now I just need a horse and I have the tusk act 4

[@RocioHernandez-lk4pc]

GOLDEN RATIO JOHNNY, UNERSTAND JOHNNY USE YOU

[@danielburt4662]

How about the bass and treble clefs in music

[@dr.joekerr119]

Happy Fibbonacci Day to all.

[@deborahedlen856]

Why does this seem similar to the mandelbrot set? How is it the same and how is it different?